Bibliography

M. Burger. X-ray Crystallography. Translated from the English by V. P. Tarasova and M. P. Shaskolskaya, edited by M. M. Umansky. State Publishing House of Foreign Literature, Moscow, 1948, 484 pp. 252 figures, 34 tables. Three editorial appendices.

The book under review is an original work devoted to an exceptionally detailed exposition of one chapter of X-ray structural analysis. The author has limited himself in many respects: he considers only those stages of X-ray analysis that consist in determining the elementary cell and the space group of a crystal; he describes only facts relating to the investigation of a single crystal; and, finally, he confines himself to considering only those methods of X-ray structural analysis in which the X-ray photograph is produced by monochromatic radiation. This last circumstance is somewhat surprising. Indeed, in principle, measurement of the crystal cell and determination of the space group can be carried out not only from rotation photographs but also from Laue photographs. However, it is quite indisputable that the Laue method is exceptionally convenient and elegant in solving, for example, such problems as finding the orientation of an unshaped crystal, refining the orientation, and determining X-ray symmetry. The Laue method is, if not necessary, then in any case an extremely useful and expedient method at that stage of investigation whose exposition is the subject of the book. It may safely be asserted that the exclusion of this section from the book is explained only by the fact that its author has not worked with this method, and decided to set forth in his book only what he himself has dealt with.

The aim of the book is to set forth methods for obtaining and interpreting X-ray photographs of single crystals. The author gives only that auxiliary material which, in his opinion, one must know to some degree when engaged in obtaining and indexing X-ray photographs. Questions of the application of one or another method remain entirely in the background. The very construction of the book is such that at the entrance the author starts from the method, not from the aim of the investigation. It is difficult to imagine a more typical accidental book devoted to the methodology of a particular experimental investigation.

The book presents work by the methods of crystal rotation and oscillation, and by methods of X-ray goniometers of various types. The author has worked in all these areas, not using all these methods for solving structural problems, but studying these methods in themselves, or ways of improving them. In almost all cases without exception the author has his own design of camera and his own method of calculating the X-ray photograph. However, the author sets forth all the existing literature, so that the reader can quite objectively judge the merits of all varieties of one or another method.

Burger’s book is in no way a textbook. It is a manual, or even a reference book, which it makes sense to study in detail when one has a specific aim before oneself. There is no doubt about the usefulness of this book: the methods

the study of single crystals acquire ever greater significance with each year, and the number of specialists working in this field is steadily growing. At the same time, in Russian (and also in foreign languages) there is not a single book devoted to the methodology of obtaining and calculating X-ray diffraction patterns.

After a brief introduction comes Ch. 2 under the title “Some Geometrical Features of Lattices”; pp. 2–3 are devoted to the concepts of crystallographic indices, and the remaining material is occupied by the theory of lattice transformation, i.e. formulas for coordinate transformations, written in a form specialized for the lattice, are discussed. In the next chapter the elementary theory of diffraction of X-rays is set forth; the author introduces the reader, in a fairly popular form, to the Laue equations, the Bragg–Wulff equations, and the concept of the structure factor. In Ch. 4 extinctions characterizing space groups are considered. The author’s logic is somewhat surprising: in Ch. 2 he sets forth elementary geometrical facts concerning the lattice, while in Ch. 4 he assumes that the concept of a space group is known. The extinction laws are derived with the help of drawings, instead of obtaining them in a few lines (and not over 20 pages) by algebraic means.

These four chapters look like an appendage written in order to justify the title of the book. The author, however, indicates in the preface that initially his plan included only a description of how to obtain and calculate X-ray diffraction patterns. Therefore, from our point of view the book begins with Ch. 5.

The presentation of the methodology of X-ray photography is conducted with exceptional detail. In Ch. 5 the author gives a “preliminary survey” of the rotation method. Then, before proceeding to the interpretation of X-ray diffraction patterns, the author acquaints us with the reciprocal-lattice method. This is done at great length: 22 pages are devoted to material that is usually set forth in three or four pages. Suffice it to say that the author does not risk introducing the concept of the reciprocal space lattice at once, but considers it necessary first to acquaint the reader with a plane square reciprocal lattice, then with a rectangular square one, after that with an oblique plane lattice, and only after spending 9 pages does he proceed to the exposition of the necessary material. The detailed elaboration, the excessive prolixity of exposition, are typical, as we shall see, of the whole book: the author does not believe that the reader possesses elementary mathematical ingenuity.

Ch. 8 is devoted to the interpretation of X-ray diffraction patterns. First of all, the author scrupulously derives formulas connecting the coordinates of a node of the reciprocal lattice with the coordinates of an interference spot on the film. This is done in two paragraphs, one of which is called “Transformation from reciprocal-lattice coordinates to film coordinates,” and the second “Transformation from film coordinates to reciprocal-lattice coordinates.” The editor of the translation informs us that he has omitted a number of elementary intermediate mathematical derivations. However, it seems that one could have acted more decisively, leaving, on average, one fifth of the author’s formulas. In Ch. 8 the indexing of rotation X-ray diffraction patterns is considered. After this, the last paragraph reports what is well known to every X-ray crystallographer, namely, the unsuitability of the rotation X-ray diffraction pattern for indexing. A special chapter is devoted to practical questions of the rotation method. All the information given here is very useful. The only reproach that can be made to the author is once again that of an utterly excessive verbosity. Next comes the chapter on the rocking method. It ends with a description of the author’s special, rather ingenious camera, which, apparently, is intended to replace an exceptionally simple camera for photographing Lauegrams. The author, however, necessarily wishes to manage by a monochromatic method.

Ch. 11 is an introduction to methods with a moving film, Ch. 12 is an introduction to the Weissenberg method. Both chapters are very well written. Ch. 13 sets forth, with exceptional detail, the interpretation of X-ray diffraction patterns, obtained—

investigated by the method of the perpendicular beam. The author’s love of detail goes very far here as well. For example, at the beginning of the chapter he tries to prove to the reader that in decoding we reproduce the plane of the reciprocal lattice in that orientation in which it was located before the start of rotation (a completely vacuous assertion). The next two chapters are devoted to other varieties of the Weissenberg method. If one sets aside the reproach that applies to the entire book—excessive detail, the exposition, alongside essential questions, of a number of quite unimportant particulars—then one must acknowledge the great value and thoroughness of the description of all the possibilities of the Weissenberg method, which continues to remain the basic method of work of the X-ray crystallographer. The author gives a considerable number of tables and graphs which will be of great service to a person beginning work in the field of obtaining Weissenberg X-ray photographs. Ch. 16 is devoted to the methods of Sauter and Schiebold. Sauter-type goniometers have begun to be produced in Leningrad only recently. Therefore this chapter will be useful to the Soviet reader. The same applies to Ch. 17, in which the principles of work by the Bouman and De Jong method are described. Moscow has begun to manufacture cameras for work by this method. Thus, simultaneously with the introduction into laboratory life of new cameras, whose importance for the development of X-ray structural analysis is difficult to overestimate, the investigator receives at the same time a good description of the principles of work by these methods. In these chapters, as in the chapters devoted to the Weissenberg method, the author gives the graphs and tables necessary for the work.

We indicated above that the first four chapters are an appendage to the main content of the book; with regard to the last chapters one must say the same thing. The content of Ch. 18, entitled “Geometry of oblique cells,” and Ch. 19, entitled “Experimental determination of lattice constants of non-orthogonal crystals,” is exceedingly trivial. The latter chapter sets forth complicated artificial methods which are not used in practice. At the same time these methods are quite simple to understand, and therefore their exposition from every point of view is excessive. Ch. 22, entitled “Theory of the interpretation of the projection of the reciprocal lattice,” likewise represents, in the main, an undesirable complication of simple matters. In this chapter the author shows how one may recognize the Laue symmetry class from the appearance of Weissenberg X-ray photographs, and then how, with the aid of the same X-ray photographs, the type of space lattice may be determined. This material is set out on 20-odd pages of fairly “dense” text. The result is illustrated by numerous tables. However, it is quite obvious that one will never have to resort to such a method of recognizing the symmetry class or the lattice type in the course of an investigation. As is set forth in this same book, all data on the symmetry of a crystal that can be obtained from X-ray experiments follow from consideration of extinction conditions. At the same time it is impossible to imagine a case in which an investigator would confine himself to consideration of Weissenberg X-ray photographs without resorting to their indexing. If it is necessary to obtain information only about the lattice type, then there exist considerably simpler methods for this than photographing Weissenberg X-ray photographs.

The “reciprocity relations” examined in detail are completely trivial. They all follow at once from the basic definition of the reciprocal lattice and are self-evident. In this chapter, in our opinion, only the last two paragraphs have a right to exist, where useful information is given on the choice of convenient reciprocal-lattice cells in various crystallographic systems and certain features of the “body of the reciprocal lattice” (G. S. Zhdanov’s terminology) are considered.

The editor has supplied the book with three very useful additions. Tables of extinctions are given for determining X-ray groups, compos-

... introduced by G. S. Zhdanov and B. A. Pospelov; a description is given of the NIIF oscillation camera (incidentally, this camera is considerably more convenient than the models considered in the text); and, finally, statistics are given for the distribution of crystals by crystal systems.

Every praise should be given to the translators and the editor. The translation has been done superbly: in the book, literally nowhere can one find reproaches either against the literary style or against the technical language. The editor has supplied the monograph with the necessary references to books and articles by Soviet authors. One can reproach only those responsible for the Russian edition for excessive reverence toward the author. The book would undoubtedly have gained if it had been subjected to substantial abridgment.

As we have already noted several times, the excessive detailing and the encumbering of the book with practically uninteresting, trivial material are the only, though not small, defect of the monograph under review. However, the presence in the book of material appearing in Russian for the first time on the methods of obtaining and calculating X-ray diffraction patterns, the exposition of this material with full knowledge of the subject, and the availability of a large number of practically valuable tables, graphs, and recommendations make it possible unreservedly to welcome the appearance on the book market of Buerger’s monograph.

A. I. Kitaigorodsky